Referring now to FIG. 1, an exemplary control system 10 includes an input signal X (i.e. a target response of the control system 10), an output response signal Y, and an error signal E. A control module 12 controls the output response signal Y based on the error signal E. The error signal E is a difference between the input signal X and the output response signal Y. In other words, the control module 12 attempts to control the output response signal Y to “follow” the input signal X. The control system 10 can be described as:Y=E*H; andE=X−Y, where H represents a transfer function of the control system 10. Each of the values X, Y, and E is a vector that includes values that occur over time.
Referring now to FIG. 2, a control system 20 typically includes a disturbance N (e.g. noise). For example, the disturbance N may be introduced into the control system 20 due to performance, manufacturing, and/or environment imperfections. The disturbance signal N is added to the output response signal Y to model the effects of the disturbance N on the control system 20. The result is a final observable response signal Z. The control system 20 can be described as:Y=E*H; Z=Y+N; andE=X−Z. In other words, due to the presence of the disturbance signal N, the output response signal Y is not observable.
The disturbance signal N may include a random component (e.g. random noise) and/or a repeatable component (e.g. a recurring disturbance due to a constant system imperfection). Typically, effects of a random disturbance signal N are non-correctable. For example, mitigating the effects of a random disturbance signal N may be limited to selecting a different transfer function H and/or changing other parameters of the control system loop.
A repeatable component in the disturbance signal N is referred to as “repeatable run-out” (RRO). For example, a hard disk drive (HDD) is a magnetic data storage medium that includes a rotating disk. A read/write head reads data from the disk and/or writes data to the disk as the disk rotates. When the disk rotates at high speeds, imperfections in the HDD and/or the disk may cause errors in position detection and control of the read and write heads.